Surface Pro 4 screen flickering and shaking

That's the well known Surface Pro 4 flicker, and the bit about it getting worse when warm is the giveaway. It's a hardware fault in the display, not something a driver fixes, though it doesn't hurt to run Windows Update and grab the latest firmware first just to be sure. You'll see people saying to put it in the freezer. It does stop the flicker for a while, which basically confirms it's heat related, but it's not a fix and the condensation risk isn't worth it. Real fix is a screen replacement, and on that model the screen and digitiser come as one part, so get a price before deciding whether it's worth it on a device that old.